Problem: The first team member in a $3$ -person relay race must run $2 \dfrac{1}{4}$ laps, the second team member must run $1 \dfrac{1}{2}$ laps, and the third team member must run $3 \dfrac{5}{8}$ laps. How many laps in all must each team run?
Explanation: To find the total number of laps, we can add. $2\frac{1}{4}$ $1\frac{1}{2}$ $3\frac{5}{8}$ first runner second runner third runner Total laps ran ${2 \dfrac{1}{4}} + {1 \dfrac{1}{2}} + 3 \dfrac{5}{8}} = \text{ total number of laps}$ Our denominators need to be the same so we can add. What is the least common multiple for the denominators $4$, ${2}$, and $8}$ ? The least common multiple of $4$, ${2}$, and $8}$ is ${8}$. $\dfrac{{1}\times 2}{{4}\times 2} = {\dfrac{2}{8}}$ $\dfrac{{1}\times 4}{{2}\times 4} = {\dfrac{4}{8}}$ Now we can add our fractions. $\begin{aligned} &{2} &{\dfrac2{8}}\\\\ &{1}&{\dfrac{4}{8}}\\ +&3}&\dfrac{5}{8}}\\ \hline\\ &&{\dfrac{11}{8}}\\ \end{aligned}$ We can replace $ {\dfrac{11}{8}}$ with $1 {\dfrac{3}{8}}$. $\begin{aligned} &1\\ &{2} &{\dfrac2{8}}\\\\ &{1}&{\dfrac{4}{8}}\\ +&3}&\dfrac{5}{8}}\\ \hline\\ &&{\dfrac{3}{8}}\\ \end{aligned}$ Now we can add our whole numbers. $\begin{aligned} &1\\ &{2} &{\dfrac2{8}}\\\\ &{1}&{\dfrac{4}{8}}\\ +&3}&\dfrac{5}{8}}\\ \hline\\ &7&{\dfrac{3}{8}}\\ \end{aligned}$ Each team will run ${7 \dfrac{3}{8}}$ laps. This can also be written as ${\dfrac{59}{8}}$ laps.